Abacus vs PAO?

For mental math is there a consensus on whats better?

Instinctively I feel like PAO would be better for longer problems and mental abacus would be better for quicker problems that are less intensive on memory and more on calculation but on the other hand there is the problem of trying to encode 3 digit numbers using PAO so I honestly have no idea.

(I guess i should mention that my primary motivation for learning mental math is to try to get a better grasp on arithmetic because even though i know how to solve +,-,x,/ I don’t feel like I truly understand it so I always feel uncertain of my answers)

For speed, you want a visual method. This can be abacus/soroban, or simply visualizing the numbers directly as most of us do, including the world’s fastest at multiplication.

Memory techniques such as PAO are only useful for extreme problems where the RAM requirement can’t be circumvented. For example:

  • Calculating exotic roots using the *logarithm method
  • Multiplying several numbers together, e.g. 234 × 456 × 678 × 890
  • Adding or multiplying two long numbers when they are spoken to you rather than written down

I don’t know of any mental calculators who have tried this seriously, but it would be an effective method.

For multiplying numbers usually, you simply use *criss-cross multiplication. For *square roots, *cube roots, *large divisions, etc. there are standard techniques that don’t require much memory at all.

All the techniques with an asterisk (*) are explained in articles linked via here: Advanced Calculation Methods – World Mental Calculation

1 Like

Dear sir , can u tell me how I can develop visual method as I do a alot of subvocalisation